The Swedish Pentecostal newspaper Dagen ("The Day") has made a survey of what the different religions and denominations will do with same-sex couples coming to them, asking to be married. Not surprisingly, most didn't want to perform such a ceremony. The by far largest denomination in the country, the (Lutheran) Church of Sweden, is, however, positive to this development. And then there is the third group, who haven't made their minds up yet.
The list of the different religious groups can be found here in Swedish (http://www.dagen.se/dagen/article.aspx?id=182259), but to mention some:
YES:
The Church of Sweden
The Jews
The Quakers
NO:
The Roman Catholic Church
The different Orthodox churches
The free churches, including e.g. Pentecostals, Seventh-Day Adventist, Methodists, the Salvation Army and some Lutheran organisations
The Moslems
The Mormons
The Jehovah's Witnesses
DUNNO:
Anglicans
Baptists
Baha'i
The Scientology Church
Some Lutheran organisations
There is also the question what to do with consciencious objectors, i.e. pastors who refuse to marry same-sex couples.
In many of the above religious groups, there is an ongoing discussion about the right to perform marriages - should our church retain that right or give it up? Does the right to perform marriages include an obligation for the individual pastor to do so? Should the right to perform marriages no longer be a question for a whole denomination, but rather given individually to those pastors who have no objections to marrying anyone that the state deems worthy? These questions are far from being solved.